Green’s Dictionary of Slang

1. of a statement or individual, pretentious.

1684		Eve Revived 99: The Man [...] observed in the Baroness so easie an Air and manners so agreeable in their Liberty, that he could not imagine ought else, but that she was some high-flying Miss.
1824		J. Wight Mornings in Bow St. 100: [A] person whom he described as a high-flying linen-draper, carrying on business in Parliament-street.
1885		‘’Arry on ’onesty’ in Punch 31 Jan. 60/1: The ’igh-flying crickits may splutter, the sleek soapboard crawlers may sniff.
1913		E.L. Warnock ‘Terms of Approbation And Eulogy’ in DN IV:i 23: Those sound like high-flying ideas.
1957		(con. 1943) A. Myrer Big War 102: Big, high-flyin’ talk twenty-four hours a day.

2. politically or socially conservative, i.e. High Church, Tory, Jacobite.

1722		R. Wodrow Analecta II (1842) 357: Ther was a designe formed among some of the rigid and High-flying Cameronians, to assasinat the Indulged Ministers in the shire of Air, at their houses, in one night, by different partys [sic].
1856		Chester Chron. 27 Sept. 8/1: Highflying Churchmen [...] we always think it convenient to protest against such high-flying assumptions.

3. (US) arrogant, pretentious.

1855		W.G. Simms Forayers 161: Come! Polly, no highflying airs with me.
1887		Hartlepool Mail 3 Aug. 4/3: ‘Highflying’ Youths [...] were each ordered to pay 5s 6d costs for gaming with cards.
1913		E.L. Warnock ‘Terms of Approbation And Eulogy’ in DN IV:i 22: high-flying. Pompous, pretentious. [...] ‘Those are high-flying people.’.
1913		Eve. Teleg. (Dundee) 18 Dec. 1/3: The working men complained that nurses sent sometimes were too highflying and required a servant and special food.

4. pertaining to luxury, wealth.

1961		‘Duncan Lee’ Castro Assassinated (2009) 132: Women [...] were part of the rewards of the business – expensive, high-flying, one-night gigs.
2000		Lehr & O’Neill Black Mass 78: It was the dawn of what would soon become known as the high-flying 1980s, the ‘Me Decade’.